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Misphasing stacks

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Subject: Misphasing stacks
From: (L. B. Cebik)
Date: Wed, 12 Feb 1997 20:56:08 -0500 (EST)
Misphasing of stacked beams:  There are two questions one can ask.  1. Is
something wrong when stacked beams are misphased?  2.  Can I do anything
useful by reversing the phase of one of a stack of beams.

To see what might happen, I modeled the same 3-element Al 20 meter beam as
in the last report over S-N ground .005/13 on EZNEC/4.  I added
transmission lines--1/4 wl section joined to form a feedpoint.  Since NEC
feedlines are mathematical, not physical, I simply used the sections to
transform the 25 ohm resonant Z of the individual beams to 100 ohms each,
in parallel for a pair of beams making 50 ohms.  This provided a baseline
for watching variations.

The 3-3 stack used 1/2 wl separation, again at 70' and 105' (which may be
translated for any upper HF band in terms of wavelengths of height and
separation)  Here are the results:
TO angle      Gain (dBi)     F-B ratio (dB)     Beamwidth      Feed Z
 (degrees)                                       (degrees)      (R+/jX)
  10           15.83           20.8               60           50.6 - 2.8

As predicted in model construction, the transmission line transformers
yield a very matchable condition.

  50           12.34           18.9               82 (oval)    45.9 + 6.4
  25           11.47           28.8               66
Reverse phasing produces two major lobes in the elevation pattern at the
indicated angles, each down at least 3.5 dB from the main lobe of the in-
phase model.  Both lobes are quite high relative to desired dx angles. 
However, such a configuration, if switchable, might be useful for a
domestic contest.  The upper lobes on the in-phase model are down by 7 dB
or more.

I next tried a 3-3-3 stack at .5-1.0-1.5 wl (70'-105'-140').  I again used
1/4 wl transmission line transformers joined at a distant feedpoint,
resulting in an anticipated baseline feedpoint impedance of 33.3 ohms R. 
Since throughout the exercise I used 41 segments per 1/2 wl to ensure
convergence without having to recheck each model, the 370-segment model was
the limit of my efforts.  Here are the results.

TO angle      Gain (dBi)     F-B ratio (dB)     Beamwidth      Feed Z
 (degrees)                                       (degrees)      (R+/jX)
    8          17.3            21.7               60           32.7 - 1.7

This result tallies well with expectations.  Notable in the 3-beam stack is
a return of some of the F-B ratio lost in the 2-beam stack.  The stack has
lesser lobes at 26 degrees (down 8.5 dB) and at 41 degrees (down 15 dB): 
these figures are given for comparison with lobes, both main and secondary,
of the same stack with one of the beams out of phase with the other two.

Highest out-of-phase:
   17          13.5            21.3               62           33.8 + 1.2
   36          13.2            29.2               68
Although the gain of each lobe is no more than that of a single beam, the
elevation angles may also be useful for domestic work.  The feedpoint
impedance is quite usable.

Middle out-of-phase:
   55          13.3            14.5               88            27.7 + 8.0
This configuration may be least useful due to the very high angle of the
main lobe.  There are lesser lobes at 8 degrees (down 6 dB) and at 33
degrees (down 4.5 dB).  The feedpoint impedance is down 18% on the
resistance side, with a significant reactance, which may show an
undesirable rise in SWR in a switched system, even after the anticipated 33
ohms is matched back to a 50-ohm cable.

Lowest out-of-phase:
   22          14.3            21.6              62             34.1 + 1.0
This configuration shows lesser lobes at 7 degrees (down 4 dB) and at 28
degrees (down 3.5 dB).  The feedpoint impedance is acceptable.  The
configuration may be useful as an alternative dx configuration, despite the
loss of gain from in-phase maximum, since--under some circumstances--
capturing the proper elevation of signal angle may be more important than
raw gain.

The exercise strongly suggests that a switchable phasing system may prove
useful, depending upon one's operating goals and activities.  Although some
options may yield less than useful patterns, most of the patterns--
especially in terms of altered elevation angles of maximum radiation--have
a certain utility.

I suspect that the upshot to consider is this:  If you are going that high
with that much rotatable metal, you might as well throw in a phase-reversal
switching system, just in case . . ..

And that is using only 3-element Yagis as the foundation.  There is no
reason to believe that results for larger individual beams cannot be
extrapolated with reasonable reliability--or that 5/8 wl spacing will not
show similar small gains above 1/2 wl spacing.  In the latter case,
however, phase reversal patterns might differ, since beam interaction
differs a bit.

Hope this data is useful, at least in setting up reasonable expectations.



L. B. Cebik, W4RNL         /\  /\     *   /  /    /    (Off)(423) 974-7215
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